Measures and solids · Ages 14–15

Arc length worksheet

Part of: Arc lengths & sectors

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Measures and solids · Ages 14–15

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The sector in the picture has a radius of 12 cm and an angle of 240° at the centre. What is its arc length, in terms of π?
Answer:
2.Taking π as 3.14, what is the arc length of the sector in the picture (radius 3 cm, angle 60°), in cm?
Answer:
3.Taking π as 3.14, what is the arc length of the sector in the picture (radius 9 cm, angle 60°), in cm?
Answer:
4.The sector in the picture has a radius of 9 cm and an angle of 240° at the centre. What is its arc length, in terms of π?
Answer:
5.The sector in the picture has a radius of 15 cm and an arc of 12π cm. What is its angle at the centre, in degrees?
Answer:
6.The sector in the picture has a radius of 22 cm and an angle of 40°. Correct to 1 decimal place, what is its arc length, in cm?
Answer:
7.A clock's minute hand is 14 cm long. Turning from 12 to the 45-minute mark, it turns °, and its tip travels π cm.
Fill in each blank
Answer:
8.Sector P has a radius of 14 cm and an angle of 90°. Sector Q has a radius of 18 cm and the same arc length as P. What is Q's angle, in degrees?
Answer:
9.The sector in the picture has an angle of 210° and an arc of 24.5π cm. What is its radius, in cm?
Answer:
10.The sector in the picture has an angle of 90° and an arc of 5.5π cm. What is its radius, in cm?
Answer:

11.A sector has an angle of 300° at the centre. What fraction of the whole circumference is its arc?
- A. 16
- B. 3
- C. 56
- D. 53
Choose the right answer
Answer:
12.A sector of radius 12 cm and angle 60° has an arc length of 2π cm.
True or false?
Answer:

13.A folding fan has ribs 25 cm long and opens out into a sector with an angle of 180°. The arc along its edge is π cm in terms of π, and cm taking π as 3.14.
Fill in each blank
Working:
Answer:
14.A bend in a road is an arc of a circle of radius 310 m, with an angle of 90° at the centre. A car drives along the bend 2 times (one way each time). To the nearest metre, how far does it drive, in m?
Working:
Answer:
15.A pendulum hangs on a string 96 cm long, and swinging from one side to the other the string turns through 29°. Correct to 1 decimal place, how far does the bob travel, in cm?
Working:
Answer:
16.A wheel of radius 23 cm rolls along the ground without slipping and moves 138π cm. Find how many degrees it turns: put the steps in order.
- A. Angle = 3 × 360° = 1080°
- B. Turns = 138π ÷ 46π = 3
- C. Circumference = 2π × 23 = 46π
Write the letters in the right order
Working:
Answer:
17.A folding fan has ribs 18 cm long and opens out into a sector with an angle of 150°. The arc along its edge is π cm in terms of π, and cm taking π as 3.14.
Fill in each blank
Working:
Answer:
18.A wheel of radius 38 cm rolls along the ground without slipping and moves 380π cm. Find how many degrees it turns: put the steps in order.
- A. Angle = 5 × 360° = 1800°
- B. Circumference = 2π × 38 = 76π
- C. Turns = 380π ÷ 76π = 5
Write the letters in the right order
Working:
Answer:

Show the answers and working

Arc length worksheet: Answers and working

1. 16 π cm
Arc = 240360 × 2π × 12 = 240360 × 24π = 16π cm.
2. 3.14 cm
In π first: 60360 × 2π × 3 = 1π, then put in 3.14: 3.14 cm.
3. 9.42 cm
In π first: 60360 × 2π × 9 = 3π, then put in 3.14: 9.42 cm.
4. 12 π cm
Arc = 240360 × 2π × 9 = 240360 × 18π = 12π cm.
5. 144°
θ360 × 2π × 15 = 12π, so θ = 12 × 180 ÷ 15 = 144°. Or: what share of the circumference 2π × 15 the arc is, times 360°.
6. 15.4 cm
Arc = 40360 × 2π × 22, worked out with the calculator's π and rounded: about 15.4 cm.
7. 270, 21
60 minutes make 360°, 6° a minute: 45 × 6 = 270°; the arc is 270360 × 2π × 14 = 21π cm.
8. 70°
P's arc is 90360 × 2π × 14 = 7π cm; for Q, θ360 × 2π × 18 = 7π, so θ = 7 × 180 ÷ 18 = 70°. Radius and angle go inversely: 14 × 90 = 18 × 70.
9. 21 cm
210360 × 2πr = 24.5π, so r = 24.5 × 180 ÷ 210 = 21 cm.
10. 11 cm
90360 × 2πr = 5.5π, so r = 5.5 × 180 ÷ 90 = 11 cm.

11. C. 56
300° is 300360 = 56 of the whole 360°, so the arc is 56 of the circumference.
12. False
Arc = 60360 × 2π × 12 = 4π cm: the circumference is 2πr, not πr nor 4πr.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 25, 78.5
180360 × 2π × 25 = 25π cm; 25 × 3.14 = 78.5 cm.
14. 974 m
One way is 90360 × 2π × 310 m; 2 times that, rounded only at the end: about 974 m.
15. 48.6 cm
The bob moves along an arc: 29360 × 2π × 96 ≈ 48.6 cm.
16. C → B → A
One turn moves one circumference, 46π cm; 138π is 3 turns, 1080°.
17. 15, 47.1
150360 × 2π × 18 = 15π cm; 15 × 3.14 = 47.1 cm.
18. B → C → A
One turn moves one circumference, 76π cm; 380π is 5 turns, 1800°.

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